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math.AP2018
W^{1,p}-solutions of the transport equation by stochastic perturbation
David A. C. Mollinedo
We consider the stochastic transport equation with a possibly unbounded Hölder continuous vector field. Well-posedness is proved, namely, we show existence, uniqueness and strong s…
math.PR2018
Existence and smoothness of the density for the stochastic continuity equation
David A. C. Mollinedo, Christian Olivera, Ciprian A. Tudor
We consider the stochastic continuity equation driven by Brownian motion. We use the techniques of the Malliavin calculus to show that the law of the solution has a density with re…